Arithmetic & Geometric Progression
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Q1: An arithmetic progression has n terms and common difference d, where d > 0. Prove that the difference of the sum of the last k terms and the sum of the first k terms is (n - k)kd.
Q2: Given that p = (x^2) - 2x - 1, q = (x^2) + 1, r = (x^2) + 2x -1, find all the real values of x for which
i) p, q, r are in arithmetic progression;
ii) (p^2), (q^2) and (r^2) are in geometric progression.
Q3: Given that Sn denotes the sum of the first n terms of a certain arithmetic progression in which the common difference is not zero and that S2n = kSn for all values of n, find the value of the constant k.
Thank you very very much!